Paper IAA-95-IAA.4.1.102
Presented at the 46th International Astronautical Congress, October 1995,
Oslo, Norway
Small Laser-propelled Interstellar Probe
Geoffrey A. Landis
Ohio Aerospace Institute
NASA Lewis Research Center 302-1
21000 Brookpark Road, Cleveland, OH 44135 U.S.A.
Background: Cost of Interstellar Flight
Recent reviews of interstellar flight have underscored the immense
cost of even a small interstellar probe. Mileikowsky (1994), for
example, calculates the cost of a 1000 kg interstellar flyby probe
traveling at 0.3 times the speed of light. Analyzing the laser-pushed
lightsail propulsion system proposed by Forward (1984), 65,000 GW must be
supplied to the laser for 900 hours. At a capital cost of $2/W, the
electrical generation facility capital cost comes to 130 trillion (1.3
10^14) dollars. Andrews (1993) calculated similar numbers, but notes
that lower electrical generating costs could reduce the price.
The cost is, of course, enormously sensitive to electrical price.
Electrical costs are discussed in more detail in the appendix.
Antimatter [Forward 1991] and particle-beam-pushed propulsion
[Landis 1989, Andrews 1993] systems, as analyzed by Mileikowsky, are even
higher in expense. Since the technology for these propulsion systems is
less developed, in this paper I will constrain the analysis to only the
case of laser-pushed lightsail propulsion.
It is clear that the energy cost of even a small interstellar probe
is likely to be huge. Hence, it is the purpose of this study to examine
the interstellar flyby mission in more detail and to design a probe
system which minimizes the required energy cost.
Baseline Mission Description
I will assume that the reader has a general familiarity with the
literature on interstellar flight. A good introduction to the problems
of interstellar flight can be found in Mallove and Matloff (1989).
In this paper I will consider variations on the laser-propelled
lightsail flyby probe first analyzed by Forward in 1984.
The propulsion system consists of a large, stationary laser of
extremely high power. In order to achieve the low divergence required,
the laser is focussed by a lens. Forward assumes a lens of 1000
kilometer diameter. This large diameter lens is constructed as a Fresnel
zone-plate, or "O'Meara para-lens"; that is, as a series of rings of
ultra-thin transparent plastic sheet, alternating with vacuum. The
transparent sheets are chosen to have a thickness exactly chosen such
that the delay of the wavefront at each element is one half of the light
wavelength. Since the lens structure is extremely flimsy, the structure,
although a third the diameter of the moon, has a mass of only 560,000
metric tons.
The large lens is required because of the fundamental divergence of
a light beam emitted from a finite aperture due to diffraction. The
minimum spot size which can be achieved, Dspot, at a distance d from the
lens, is:
Dspot = 2.44 d (lambda)/Dlens (1)
where (lambda) is the wavelength of the light used. This equation
defines the diameter of the first zero of the Airy diffraction pattern;
84% of the light is contained within this circle. Any units can be used
for d, (lambda), and Dlens as long as the same units are used
consistantly; it is convenient here to use meters.
The laser power is focussed onto a spacecraft consisting of a thin
reflective "sail" plus a small payload. By Einstein's relation, the
amount of momentum in a light beam of energy E is:
p = E/c (2)
By reflecting the incident light, a momentum is transferred to the
sail equal to twice the momentum of the incident photons (neglecting, in
this approximation, the relativistic correction due to redshift, small
the the speed considered). In conventional terms, this produces a force
6.7 newtons per gigawatt. While this is an extremely low force by the
standards of the rocket-based systems used for conventional spaceflight
systems, no reaction mass at all is expended. This makes the lightsail
system extremely attractive for interstellar missions, which would
otherwise require prohibitive mass-ratios to accomplish.
The reflective sail is assumed to consist of an ultra-thin foil of
aluminum, plus structural elements required to keep the sail roughly
flat. Solar sails, which operate by reflection of sunlight, have been
extensively considered in the literature. The sail analyzed by Forward
differs from most proposed solar sail designs in that most solar sail
designs typically assume that the reflective (aluminum) layer is a thin
coating on a plastic (e.g., Kapton) sheet. Forward assumes that the
plastic sheet can be elimiated, and that the aluminum alone is sufficient
to serve as the structure. Forward also assumes that the aluminum layer
is extremely thin, considerably thinner than that used by most solar sail
proposals, in order to minimize the mass required.
The probe analyzed by Forward reaches a top speed of 0.11 c,
somewhat lower than the speed analyzed by Mileikowsky. Parameters for
the baseline mission are shown in Table 1. While the reference also
considers other mission concepts which decelerate to a stop at the
destination, the simple fly-by probe analyzed does not. Travelling at
11% of the speed of light, the Forward probe requires 40 years before
arrival at Alpha Centauri. Including three years for acceleration and
four years for the information sent by the probe to return, results from
the Forward flyby probe can be expected 47 years after the start of the
mission.
Table 1
Reference laser-pushed lightsail flyby mission
Mission
Velocity 0.11 c
acceleration 0.36 m/sec^2 (thermally limited)
distance at laser cutoff 0.17 LY (1.6 10^12 km)
Laser
Laser wavelength 1000 nm
Lens diameter 1000 km
Laser power 65 GW
Laser pulse duration 3 years
Total laser power 1.7 10^12 kW-hr
Sail
diameter 3.6 km
area 10.2 km^2
material Al
thickness 16 nm
thermal emissivity e 0.06
temperature 600 K (2/3 of Tm)
material density (D) 2.7 gr/cm3
reflectivity 82%
Mass
Total mass 1000 kg
Areal density (total) 0.1 g/m^2
Sail 0.043 g/m^2
Structure 0.03 g/m^2
payload 0.027 g/m^2
Note that the electrical power of 650 GW required, assuming laser
efficiency of 10%, is a hundred times less than the 65,000 GW assumed by
Mileikowsky. This is partly due to the fact that the Forward probe speed
is only one third as high, but primarily due to the fact the laser on
time is 30 times longer than the time assumed by Mileikowsky.
Nevertheless, the generating capacity required would cost 1.5 trillion
dollars at today's power cost, and 37 billion dollars at the assumed
evolutionary values for power generation cost discussed in the appendix.
This paper analyzes approaches to reducing the total power required
for an interstellar fly-by mission propelled by a laser-pushed lightsail
without increasing the mission time. The constraints assumed no advances
in physics beyond that currently known, and no technology advances beyond
that now available (except for the lens and sail technology assumed in
the baseline paper).
Alternative Technologies
The propulsion system described is achievable entirely within the
currently known laws of physics, however, it requires significant
advances in engineering. First, it requires development of large laser
systems. Second, it requires the ability to fabricate gossamer
structures of a thousant kilometers in diameter with the control to
position the structure to within a few meters. Third, it requires the
ability to fabricate a reflective film without a plastic substrate.
The Forward mission scenario has been analyzed, and several
difficulties pointed out, by Andrews and Zubrin (1988) and by Landis
(1989).
Of these technologies, the thousand-kilometer diameter para-lens is
probably the most speculative, in particular considering the stringent
positioning requirements. As noted by Landis (1989), the lens and the
laser source are both required to be positioned to within an accuracy of
3 meters to maintain a beam wander of less than the sail radius at a
distance of 0.17 LY. If the beam wander is slow, the probe can correct
by detecting the beam and moving laterally to maintain correct
positioning. However, to bring the technology closer to realization, it
would be desirable to (1) reduce the required size of the lens, and (2)
reduce the required focal distance.
Landis (1989) also notes that optics considerations show that the
laser aperture will be magnified at the optical image plane. However, as
noted by Forward (1985/1989), as long as the laser maintains
diffraction-limited coherence across the aperature, it is possible to
focus the beam to a spot actually smaller than the magnified image of the
laser aperture. This criticism thus reduces to a requirement for high
coherence of the laser, and not a fundamental physical limitation on the
technology.
It is occasionally suggested that the requirement for the laser
could be eliminated by directly focussing solar energy on the sail with a
large lens. Unfortunately, this does not work. Focussing lenses cannot,
in principle, produce power density at the sail higher than solar
intensity unless the diameter of the focussing lens is larger than the
apparent diameter of the sun. This is because the energy density per
unit solid angle cannot be changed by a lens or any combination of
lenses. Unless the lens diameter is comparable to the diameter of the
sun, there is little advantage to using a lens at all. An alternative is
to simply eliminate the lens system entirely, and to use a solar-sail
propulsion. This has been analyzed in detail by Matloff (1984) and
Mallove and Matloff (1989).
Since the Forward probe mass is dominated by the sail and the
structural system which supports it, merely reducing the payload
requirement does not significantly reduce the probe mass. When the sail
mass is reduced, the payload can be proportionately reduced. Thus, I
adopt the scaling rule used by Forward: structure plus payload mass = 1.3
times sail mass. This assumption will be examined in more detail later.
One alternative considered was to replace the solar sail by a
photovoltaic array, and to use the power generated to run an electric
propulsion system, such as an ion drive. This concept was analyzed by
Landis (1994), and shown to produce, at best, only small improvements
over the reference system. It will not be analyzed in detail here.
Beam spread could be lowered by increasing the focussing lens
diameter. This approach was not considered, since the O'Meara lens is
one of the critical technological improvements required, and increasing
the diameter could result in unacceptable additional cost. Only
improvements which decreased lens diameter were considered.
Three changes were analyzed: changes in wavelength used, changes in
sail material, and changes in laser technology.
Wavelength
If a shorter wavelength is used, beam spread due to diffraction
decreases, and hence the sail area can be decreased. A minimum
wavelength is set by three factors: low sail reflectivity at ultraviolet
wavelengths, low laser efficiency at short wavelength, and decreased lens
transparency in ultraviolet. 500 nm is shown to be achievable.
I will assume that, when the wavelength is reduced, both the
para-lens and the spacecraft sail are reduced in equal proportions. This
would thus allow the lens to be reduced to 707 km (from 1000) and the
sail diameter to be reduced to 2.1 km (from 3.6). This results in a
reduction of the sail mass by a factor of two (and a similar reduction of
the lens mass.)
Sail Material
If the acceleration is increased, the required focus distance is
reduced, and hence the sail area can also be decreased. For acceleration
a and final velocity Vf, the distance at beam cut-off is (neglecting
relativistic corrections):
d = 0.5 vf^2/a (3)
Higher acceleration allows the same velocity to be achieved over a
lower distance. Hence, a smaller sail and thus lower power laser can be
used to achieve the same maximum velocity. It also means that the amount
of time used for the acceleration is lower.
Acceleration is limited by the thermal capability of the sail, due
to the fact that the sail material is not perfectly reflective, and the
amount of light which is absorbed by the sail will result in heating.
The thermally limited acceleration is (Forward 1984):
a = 4 R/c [e (sigma) T^4]/(alpha)Dt (4)
where R is the reflectivity, e is the emissivity, (sigma) is the
Stefan-Bolzman constant, alpha the absorption, D the density, and t the
thickness. Thus, if the reflectivity and the emissivity is constant, the
figure of merit for a given material is the fourth power of the
temperature divided by the density. All other considerations constant,
the thermally-limited acceleration possible with a sail is proportional
to the figure of merit.
A considerable increase in the amount of power which could be
applied to the sail, considered by Forward, can be made if the sail is
constructed such that the reflectivity of the rear (laser-facing) side of
the sail is high, while the thermal emissivity (e) of the front side of
the sail is high. It is not clear, however, whether this is technically
achievable without a proportional increase in mass. Thus, this solution
is not assumed here. The emissivity of materials used for sails will be
assumed to be constant at 0.06.
The Forward mission scenario assumes that the maximum operating
temperature of the sail is 2/3 of the melting temperature of the sail
material. This assumption is a reasonable estimate, and will be used as
a scaling law.
Various sail materials were considered. Several apparently
promising materials are eliminated by other considerations. Silver,
despite a melting temperature higher than that of aluminum, apparently
agglomerates at high temperature in thin-film form [Forward 1984].
Metallic tantalum and zirconium are greyish in color, indicating high
optical absorption. Boron, with high melt temperature and low density,
is a semiconductor rather than a metal; it is also greyish in color.
Table 2 shows properties and the calculated figure of merit
(compared to aluminum) for several candidate materials with better
high-temperature performance than aluminum.
Table 2: properties of metals for possible use in a lightsail
Material D Tm T^4/D
(gr/cm^3) (K) (norm. to Al)
Aluminum (Al) 2.7 940 1
Platinum (Pt) 21.45 2045 2.8
Iridium (Ir) 22.4 2683 8.
Titanium (Ti) 4.54 1950 11.0
Berylium (Be) 1.8 1550 11.1
Scandium (Sc) 2.99 1812 12.5
Niobium (Nb) 8.85 2741 22.7
Beryllium, with a melt temperature of 1550 K, is apparently an
excellent candidate of the metallic films. The exceptional high
temperature properties of beryllium sails for solar sail use was noted by
Matloff (1984).
Two metals with higher performance, due to a higher melt
temperature, are scandium and niobium. Scandium is currently an
extremely rare and costly material; perhaps it will be more available and
less costly with further development, but at the moment, it is apparently
too rare and expensive to consider. Niobium, on the other hand, is a
highly reflective metal which is industrially available in large
quantities, and is used in a number of applications, such as welding,
stainless steel, and superconductors.
Table 3 shows results calculated by using the best of these films,
compared to the baseline aluminum sail. Acceleration is calculated from
the figure of merit. For convenience, acceleration is calculated in
gravities. The beam cut-off is assumed to occur at v=0.11 times the
speed of light. From the calculation of distance, a calculation of the
sail diameter can be made.
Table 3: Thermally limited acceleration and distance travelled
Material a (g) d (LY)
Aluminum (Al) 0.036 0.17 (baseline case)
Berylium (Be) 0.42 0.015
Niobium (Nb) 0.82 0.0075
Another class of possible sail materials is the dielectric thin
film. Dielectric materials are transparent. By making a film exactly
1/4n times the wavelength of the light, the reflectivity can be quite
high (Landis, 1989). The reflectivity at this quarter wave thickness is:
R = [(n^2 - 1)/(n^2+1)]^2 (2)
where n is the refractive index of the material.
Forward (1986) considered multi-layer dielectric films, consisting
of quarter-wavelength layers of dielectric materials alternating with
quarter-wavelength spaces of vacuum. This approach can improve the
reflectance to nearly unity, however, the ratio of reflectance to mass is
maximized for single layers of quarter wavelength material, and so this
is what was considered here.
Table 4 shows three of the dielectric materials considered. Other
materials are discussed in Landis (1989). For dielectrics, the thickness
assumed is the quarter-wave (maximum reflectance) thickness for 500 nm
light. The operating temperature Top is assumed to be 2/3 of Tmelt
except for diamond, where it is 2/3 of the diamond-to-graphite transition
temperature of 1800 K. Here the figure of merit (again figured relative
to aluminum) is RT^4/tD, which accounts for the fact that the film is
partly transparent, and also accounts for the fact that the thickness,
specified as quarter wave, is not constant at 16 nm.
Table 4: properties of dielectric sails
Material D(gr/cc) n R(%) T(nm) Top(K) RT^4/tD
Diamond (C) 3.51 2.41 50 42 1200 10.3
Silicon carbide 3.17 2.65 56 29 1333 17.4
Zirconia (ZrO2) 5.41 2.15 42 47 1810 34.7
Thin diamond (or "diamond-like carbon") films are currently being
produced by a wide variety of methods. However, it is not yet possible
to produce self-standing diamond films without a substrate. Likewise it
is not clear that such films of silicon carbide films can be produced.
Silicon carbide, while posessing a high figure of merit, is also
typically not as transparent as desired. Zirconia films, with the
highest figure of merit, are currently produced using electron-beam
evaporation for optical coatings. A technology to remove the substrate
still needs to be developed.
While the figure of merit for the zirconia film is 50% higher than
that for metallic niobium, the reduced reflectivity of 42% means that
over half the light incident on the sail is lost. This means that,
despite the possible shorter acceleration distance, a zirconia sail would
require a higher laser power than a niobium sail.
The use of a simple figure of merit, however, is only appropriate if
the absorption (alpha) and the emissivity e are identical to that for
aluminum. In fact, the dielectric films are likely to have both lower
absorption and higher emissivity. This is a topic for future work,
beyond the scope of the current study.
Laser Efficiency
Third, improvements in laser efficiency were considered. Raising
the electrical to optical conversion efficiency hc directly lowers power
cost. The highest conversion efficiency lasers manufactured today are
semiconductor diode lasers. Semiconductor diode lasers available off the
shelf have demonstrated efficiency of over 40%; 60% has been achieved int
he laboratory devices (Friedman et al. 1994). Wavelengths in the blue
have been achieved, for example with ZnSe laser diodes, and 500 nm
operation should be achievable. The difficulty of using semiconductor
diode lasers is that individual lasers diodes typically have a power of
roughly 1 watt. Since it is necessary that the laser output be coherent
across the entire array aperture, it will thus be necessary to phase-lock
on the order of a billion individual emitting elements together. This
can, in principle, be accomplished by running the lasers in a MOPA
(Master Oscillator/Power Amplifier) configuration. However, the sheer
magnitude of the problem makes it a daunting technical challenge.
Another difficulty with semiconductor diode lasers is that thermal
failures mean that long operating times require temperature control to
keep the junction temperature at roughly room temperature or (preferably)
lower. This means that active thermal radiators will be required.
An alternate technology for high efficiency of laser power
generation is the free-electron laser. High energy efficiency requires
that the electron beam be recycled after the pass through the wiggler
magnets. With recycling, it is claimed that the Novosibirsk FEL
[Litvenko et al. 1994] can "easily" reach an e-beam to light conversion
efficiency which "can exceed 30%." Efficiencies of 40% and higher are
predicted as being achievable for wavelengths as low as 500 nm.
Since there are two technologies (and probably others as well) for
which electric to optical conversion efficiency of at least 40% is
achievable, this is a reasonable extrapolation to assume for an advanced
system.
Directly solar-pumped lasers are also a possibility. Landis (1994)
suggests that a directly solar-pumped semiconductor diode laser could be
achieved using existing technology, with a conversion efficiency
comparable to that of GaAs solar cells. This could further reduce the
energy cost, if the laser cost is comparable to the cost of a
similar-sized solar array. The difficulty of phase-locking large numbers
of diode lasers is similarly difficult.
Discussion
Table 5 shows the results of the application of the suggested
improvements in wavelength and material on the acceleration, the diameter
of the lens and the sail, and finally on the total (sail, structure and
payload combined) probe mass.
Table 5 Thermally limited acceleration and distance travelled
Sail Material lambda a Dlens Dsail Mass
(nm) (g) (km) (km) (kg)
Aluminum (Al) 1000 0.036 1000 3.6 1000.
(baseline)
Aluminum (Al) 500 0.036 707 2.5 500
Berylium (Be) 500 0.42 212 0.764 30
Niobium (Nb) 500 0.82 148 0.534 72
Note that, despite the higher acceleration, the niobium sail turns
out to have a higher mass than the Be sail, due to the high density of
niobium.
This calculation has assumed, again, that the reduced size allowed
by shorter wavelengths and higher acceleration are realized equally by
lowering the sail diameter and lowering the lens diameter.
The improvements over the baseline case are astonishing. Instead of
requiring a 1000 km para-lens, the lens diameter is reduced to 212 km
[for the Be sail]. The total lens mass is reduced from half a million
tons to 23,000 tons. Likewise, required pointing tolerance is loosened
by a factor of 5.
The sail area is reduced from 3.6 km to only 760 meters.
For this analysis, the payload has been considered to be a constant
27% of the probe mass. Incorporating all of the proposed changes into
the reference mission allows the Forward probe mass to be decreased from
1000 kg (including 333 kg payload) to 30 kg (8 kg payload). Is it
feasible to consider a payload as small at 8 kg? Table 6 shows the
evolution of recent spacecraft designs. The improvement in mass from 100
kg to 19 kg is slightly more then the improvement in mass from Voyager to
Pluto Flyby (25 years). A 19 kg payload may thus be feasible, if current
trends in technological improvement, around the year 2030. For a fly-by
mission, which will pass through the target solar system at high
velocity, and not orbit at short distances to the (hypothetical) planets,
the instruments of an interstellar probe will be more similar to the
Hubble telescope than to a conventional planetary probe. It would
require, for example, a large inflatable mirror of high optical quality.
Alternatively, it may be possible that the lightsail mirror itself may be
usable as the optical element for a telescope. This would probably
require an adaptive secondary lens, since the lightweight structure is
unlikely to be an optically surface of the required precision [for use as
a lightsail alone, little tolerance is required on surface quality].
Communications will also be significantly more difficult. An
interstellar probe will possibly use optical communications. This may be
done with the same optical element used for the telescope mirror.
Alternatively, the lightsail itself is a large metallized reflector; it
could be designed to be used as a dish reflector for microwave or
millimeter wave transmission. With the technology for such large
solar-sail derived reflectors as microwave receivers, and the technology
for large para-lenses as optical receivers, there should be no difficulty
in receiving and amplifying even relatively small signals over
interstellar distances.
Thus, there seem to be no physics barriers to the technological
advances required for such a spacecraft mass.
Table 3 assumes that spacecraft mass decrease will be by
evolutionary changes in technology. If revolutionary changes in
technology occur (e.g., "Starwisp"; nanotechnology), no prediction is
possible.
Table 6: Spacecraft Mass
Voyager (1977) 800 kg
Clementine (1994) 200 kg
Pluto Fast Flyby (proposed 2000+) 100 kg
Interstellar (2020 +) : ???
Table 7 shows the effect of the improvements discussed on the
required power levels. The most significant improvements come from the
reduction of the wavelength from 1 micron to 500 nm and improvement of
the laser electrical to optical conversion efficiency hc from 10% to 40%.
These two factors drop the power from 650 GW to 81 GW, a factor of 8
improvement.
The higher acceleration permitted by higher temperature and lower
density sail material requires a proportionately higher laser power per
unit area. The total power reduces proportionately to the square of the
sail area, which decreases with distance and hence to the acceleration.
If the lens area were held constant, and the sail area decreased with the
acceleration, then the total required power would decrease
proportionately to the improvement in acceleration. The design rule
used, however, proportioned the advantages of the shorter distance
equally to decreasing the sail and the lens diameter. The sail area thus
decreases proportionately to the acceleration. This results in no change
in the required power as the thermally limited acceleration improves.
The density is the only factor in the power. By the use of a Be sail,
the reduction in density of the material lowers the mass, allowing lower
power. The Nb sail, on the other hand, because of the high density,
actually requires a higher power level than the baseline.
Table 7: Power Required
Sail Material lambda P(laser) effic P(electr.) T
Eelectric
(nm) (GW) (%) (GW) (yrs) (GW-hr)
Aluminum (Al) 1000 65 10 650 3 17.1 106
Aluminum (Al) 500 32 10 320 3 8.5 106
Aluminum (Al) 500 32 40 81 3 2.1 106
Berylium (Be) 500 22 10 220 0.27 0.52 106
Niobium (Nb) 500 107 10 1065 0.13 1.21 106
Berylium (Be) 500 22 40 54 0.27 0.13 106
With these changes, the required power is reduced from 650 GW to 54
GW. Even assuming no reduction in power costs from today's values, and
assuming that direct solar-pumped lasers are not available, the power
generation cost is reduced by two orders of magnitude. At the
conservative cost of $2/watt, for example, the power generation cost is
roughly 100 billion dollars, comparable to the cost of the Apollo
program. At the advanced technology cost of $0.05 per watt, the cost is
only 3 billion dollars, comparable to today's the cost of a large space
mission such as Cassini. And, it must be emphasized, the power
generation facility remains in place after the launch of the Forward
probe is completed, and thus can be used either for additional prove
launches, or to provide power for other applications.
Global electrical usage in 1992 is 1200 GW. The baseline mission
requires roughly half the world generating capacity. The redesigned
mission requires about 4% of the world generating capacity. Since the
rate of growth of world electrical capacity (between 1970 and 1992) is
roughly 2.3 GW per year, the power generation capacity required is
slightly less than that produced every two years.
An alternate method to estimate electrical power costs is to look at
the total amount of energy requried, Eelectric, the power times the time.
Since the required amount of power is far less than the world generating
capacity, it is interesting to calculate the cost assuming current prices
for electrical power in the United States, which averaged 5.1! per
kilowatt hour at industrial power levels in 1992. The final number, one
hundred thirty thousand gigawatt-hours, would cost 6.63 billion dollars.
This is very reasonable for the magnitude of the mission proposed!
Conclusions
Recent reviews of interstellar flight have underscored the immense
cost of even a small interstellar probe. Mileikowsky (1994), for
example, estimates the electrical power generating cost to send a 1000 kg
interstellar flyby probe traveling at 0.3 times the speed of light as 130
trillion (1.3 10^14) dollars! Fortunately the problem turns out not to
be so severe.
In this paper the mission design for a laser-pushed lightsail probe
has been redesigned with a "smaller, better, cheaper" philosophy. Using
a shorter wavelength, more efficient lasers, and a higher temperature and
lower density berylium sail, the lens and the lightsail sizes required
can both be reduced by a factor of five, the acceleration increased by a
factor of twelve, the probe mass reduced by a factor of 33, the power
requirement reduced by a factor of twelve, and the total energy reduced
by a factor of 130 compared to the baseline mission. At today's
electrical generating costs, the energy cost to launch the interstellar
probe is only 6.6 billion dollars. This is quite reasonable for the
magnitude of the mission proposed.
Additional improvements possible by using a dielectric material
instead of a metal for the sail have not yet been quantified.
An interstellar probe is feasible with technology known today.
Appendix: Power Cost
Mileikowsky (1994) notes that a one thousand kilogram probe
traveling at 0.3 c has a kinetic energy of 1,180 billion kilowatt hours.
Analyzing the laser-pushed lightsail propulsion proposed by Forward
(1984), and assuming an electrical-to-light conversion efficiency of 30%,
and a light-to-probe kinetic energy conversion efficiency of 6-7%, 65,000
GW must be supplied for 900 hours. At a capital cost of $2/W, the
electrical generation facility capital cost comes to 130 trillion (1.3
10^14) dollars. At current U.S. electricity costs of 3!/kW-hr, the cost
of the power used is 1.77 trillion (1.77 10^12) dollars.
The capital cost of $2/watt is close to typical of the electrical
power industry systems in operation in the United States today, typically
coal, natural gas, and oil-fueled generators. Nuclear generating
capacity is currently slightly more expensive. The operating costs of
3!/kW-hr is slightly lower than the 1990 value for average fuel,
operating, and maintenance cost. The total cost to the industrial
consumer, calculated in 1990, including both cost of capital and
operating cost, is 5.1! per kilowatt-hour, averaged across the United
State, varying somewhat from location, slightly lower in the Northwest,
where there is a large amount of hydroelectric power, and somewhat higher
in the northeast.
Space power systems, of course, are now considerably more expensive,
typically closer to $1000 per watt.
The power generating system for such a laser system would likely be
photovoltaic. Terrestrial photovoltaic manufacturing technology is
capable of producing solar arrays in quantity at a cost of roughly
$2/peak watt, where a "peak watt" is defined as the production of one
watt of energy under full illumination of 1 kW/m^2 (i.e., noon on a
cloud-free day). However, space solar arrays are subject to considerably
more difficult requirements, such as tolerance to ultraviolet,
particulate radiation, and thermal cycling, and require lighter weight
technologies than terrestrial systems. Nevertheless, it is reasonable to
assume that space technology, at a sufficiently large (multi-gigawatt)
scale, would be able to approach (and possibly improve on) the
terrestrial cost. Thus, the $2/watt value assumed is reasonable for
systems typical of todays technology. Such a system likely would likely
produce energy without a significant operating cost, and hence the
3!/kW-hr operating cost assumed by Mileikowsky is probably not
appropriate. However, since this represents only one percent of the
energy cost, the difference is negligible.
Using terrestrial photovoltaic technology, however, lower costs may
be possible, since a large space-based system may operate closer to the
sun than the Earth's orbit, and hence at higher solar intensity.
Unfortunately, output power does not increase linearly with incident
intensity, since the conversion efficiency of photovoltaic cells
decreases at increased operating temperatures. Nevertheless, it is not
unreasonable to assume that, with innovative design of passive thermal
radiation systems, it may be possible to produce ten times higher power
levels out of photovoltaic systems by operating them at higher intensity
without huge increases in cost. This would reduce the capital cost by an
order of magnitude, from $2 to $0.2 per watt.
In 1977, the United States Department of Energy made a goal for the
Photovoltaic research program of $0.50 per watt, in then-current year
dollars. This cost was believed to be achievable, and even lower prices
of $0.10 to $0.30 possible [Maycock 1978]. While these goals are
somewhat higher expressed in current dollars, it is still evident that
the technology of low-cost solar arrays has not been developed to the
maximum extent possible, and it is likely that future solar array prices
may be considerably lower than current values. The production of
hundreds of gigawatts of power generation capability would certainly
result in highly efficient economies of scale! A factor of 4 reduction
in price with advances in technology and low-cost production methods
seems to be a reasonable, and possibly conservative, assumption. This
would bring the capital cost for space-generated electricity down to
$0.05 per watt.
The net effect of these two modifications to the baseline power cost
is to reduce the power generation cost from the $130 trillion estimate of
Mileikowsky to roughly 3 trillion (3 10^12) dollars. This is still an
unreasonable price for any mission to be feasible in the currently
existing world sociopolitical environment.
As pointed out by Andrews (1993), the power system, once built,
remains in operation after the probe is launched. Hence, the capital
cost can be amortized over many flights, to lower the per-flight cost;
alternatively, the power system can be used for other purposes, to recoup
the capital costs.
One solution is to reduce the cost of power by several orders of
magnitude, for example, by creating a space infrastructure incorporating
self-reproducing factories to produce solar cells. Andrews, for example,
considers a reduction of three to four orders of magnitude lower than
existing costs. In principle, this approach could reduce the power
generation price to the cost of making the initial self-reproducing
factory. This technology is as yet, however, still speculative.
These analyses have not included the costs of power conditioning and
distribution, which have been assumed to be negligible. An detailed
engineering analysis of a flight system would have to include such items.
An additional consideration is the laser cost. Lasers manufactured
today typically cost upwards of $1000 per watt. Clearly, lower cost
technology for lasers is necessary before lightsail propulsion can be
considered a viable technology.
References
Andrews, Dana G., and Zubrin, Robert (1988), "Magnetic Sails and
Interstellar Travel," paper IAF-88-553, 39th Congress of the
International Astronautical Federation, Bangalore, India.
Andrews, Dana G. (1993), "Cost Considerations for Interstellar
Missions," paper IAA-93-706; also presented at Conference on Practical
Robotic Interstellar Flight, New York University, August 29-Sept. 1, 1994.
Forward, Robert L. (1984), "Roundtrip Interstellar Travel Using
Laser-Pushed Lightsails," J. Spacecraft and Rockets, Vol. 21, Mar-Apr.,
pp. 187-195.
Forward, Robert L. (1985), "Starwisp: an Ultra-light Interstellar
Probe," J. Spacecraft and Rockets, Vol. 21, May-June, pp. 345-350.
Forward, Robert L. (1985/1989), private communications to G. Landis
(letters).
Forward, Robert L. (1986), "Laser Weapon Target Practice with
Gee-whiz Targets," presented at Laser Propulsion Workshop, Lawrence
Livermore National Laboratories, 7-8 July.
Forward, Robert L. (1991), "21st Century Space Propulsion," Journal
of Practial Applications in Space, Winter, Vol. 2, No. 2, 1-35.
Friedman, Herbert, et al. (1994), "Scaling of Solid-state Lasers for
Satellite Power Beaming Applications," SPIE Optics, Electro-optics &
Laser Conference, Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE
Proceedings Volume 2121, 49-57.
Landis, Geoffrey A. (1989), "Optics and Materials Considerations for
a Laser-Propelled Lightsail," paper IAA-89-664, 40th Congress of the
International Astronautical Federation, Oct. 7-12 1989, Malaga, Spain.
Landis, Geoffrey A. (1991), "Laser-Powered Interstellar Probe," APS
Bulletin, Vol. 36 No. 5, 1687-1688.
Landis, Geoffrey A. (1994), ""Prospects for Solar Pumped
Semiconductor Lasers," SPIE Optics, Electro-optics & Laser Conference,
Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE Proceedings Volume
2121, 58-65.
Landis, Geoffrey A. (1994A) "Laser-Powered Interstellar Probe,"
presented at Planetary Society Conference on Practical Robotic
Interstellar Flight, NY University, Aug. 29-Sept. 1.
Litvinenko, Vladimir N. et al., "Component Technologies for a
Recirculating Linac Free-electron Laser," SPIE Optics, Electro-optics &
Laser Conference, Los Angeles CA, Jan. 24-28; Laser Power Beaming, SPIE
Proceedings Volume 2121, 21-37.
Mallove, Eugene and Matloff, Gregory (1989), Chapters 5-6, The
Starflight Handbook, John Wiley and Sons, NY, 71-105.
Matloff, Gregory L. (1984), "Interstellar Solar Sailing:
Consideration of Real and Projected Sail Materials,: J. Brit
Interplanetary Soc., Vol. 37, Mar., 135-141.
Maycock, Paul D. (1978), "The Development of Photovoltaics as a
Power Source of Large-Scale Terrestrial Application," Proc. 13th IEEE
Photovoltaic Specialists Conference, IEEE, NY, 5-8.
Mileikowsky, Curt (1994), "Cost Considerations Regarding
Interstellar Transport of Scientific Probes with Coasting Speeds of About
0.3c," paper IAA-94-655, 45th Congress of the International Astronautical
Federation, Oct. 9-14, 1994, Jerusalem, Israel. An earlier version of
this paper was presented as Mileikowsky (1994A).
Mileikowsky, Curt (1994A), "How and When Could We Be Ready to Send a
1000 kg Probe With a Coasting Speed of 0.3c to a Star?" Conference on
Practical Robotic Interstellar Flight, New York University, August
29-Sept. 1, 1994.
____________________________________________
Geoffrey A. Landis,
Ohio Aerospace Institute at NASA Lewis Research Center
physicist and part-time science fiction writer